In our calculations, we set \(m_u=m_d=330\)  MeV, \(m_s = 450\)  MeV and \(m_c = 1483\) 
MeV for the constituent quark masses. The masses
of the well-established hadrons in the final states used in the calculations are
adopted from the PDG [1]}.
In the present work, both \(\beta \)  and the pair creation
strength \(\gamma \)  are considered as free parameters, which are determined by
fitting the decay widths of the well-established charmonium states
\(\psi (3770)\) , \(\psi (4040)\) , \(\psi (4160)\)  and \(\chi _{c2}(2P)\) .
If we adopt the wave function of a charmonium state
calculated using the LP model, we obtain \(\beta =0.380\)  GeV and \(\gamma =0.234\) .
And if we adopt the wave function of a charmonium state
calculated using the SP model, we have \(\beta =0.356\)  GeV and \(\gamma =0.217\) , which are consistent with the LP results.
With these parameters, the decay widths of \(\psi (3770)\) , \(\psi (4040)\) , \(\psi (4160)\) 
and \(\chi _{c2}(2P)\)  can be reasonably described in both LP and SP models (see Table REF ). The strong decay properties
for the higher charmonium states up to the mass of the \(6P\)  multiplet have been listed
in Tables REF -REF .
